caa a22 4500 605469954 CHVBK 20210128100325.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00500-014-1314-9 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1314-9 A Runge-Kutta method with reduced number of function evaluations to solve hybrid fuzzy differential equations [Elektronische Daten] [Ali Ahmadian, Soheil Salahshour, Chee Chan] In this paper, we employ a numerical algorithm to solve first-order hybrid fuzzy differential equation (HFDE) based on the high order Runge-Kutta method. It is assumed that the user will evaluate both $$f$$ f and $$f'$$ f ′ readily, instead of the evaluations of $$f$$ f only when solving the HFDE. We present a $$O(h^4)$$ O ( h 4 ) method that requires only three evaluations of $$f$$ f . Moreover, we consider the characterization theorem of Bede to solve the HFDE numerically. The convergence of the method will be proven and numerical examples are shown with a comparison to the conventional solutions. Springer-Verlag Berlin Heidelberg, 2014 Fuzzy ordinary differential equation nationallicence Hybrid system nationallicence Bede's characterization theorem nationallicence High order Runge-Kutta method nationallicence Seikkala derivative nationallicence Ahmadian Ali Centre of Image and Signal Processing, Faculty of Computer Science and Information Technology, University of Malaya, 50603, Kuala Lumpur, Malaysia aut Salahshour Soheil Department of Computer Engineering, College of Technical and Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran aut Chan Chee Centre of Image and Signal Processing, Faculty of Computer Science and Information Technology, University of Malaya, 50603, Kuala Lumpur, Malaysia aut Soft Computing Springer Berlin Heidelberg 19/4(2015-04-01), 1051-1062 1432-7643 19:4<1051 2015 19 500 https://doi.org/10.1007/s00500-014-1314-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1314-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ahmadian Ali Centre of Image and Signal Processing, Faculty of Computer Science and Information Technology, University of Malaya, 50603, Kuala Lumpur, Malaysia aut NATIONALLICENCE 700 1- Salahshour Soheil Department of Computer Engineering, College of Technical and Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran aut NATIONALLICENCE 700 1- Chan Chee Centre of Image and Signal Processing, Faculty of Computer Science and Information Technology, University of Malaya, 50603, Kuala Lumpur, Malaysia aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/4(2015-04-01), 1051-1062 1432-7643 19:4<1051 2015 19 500